Large distance asymptotics of correlations in lattice random fields

Talk in Mathematics
I will start by introducing the general problem (by describing what are lattice random fields,
which ones do I wish to study, where do they come from, and what are the questions I want
to discuss). Then, the general question will be illustrated by taking a specific example: the
high temperature Ising model, and I will discuss a heuristic (coming from physics) which
allows one to predict the large distance behaviour of the most important correlation
function: the two-point function. In this example, I will describe in an informal and nontechnical
way how one can put the general heuristic on rigorous ground, and state a few
results as illustrations.
Finally, I will briefly mention further applications of the developed methods to both the
study of general correlations, and to the study of 2D interfaces.
Based on (a sequence of) joint work with Y. Aoun, D. Ioffe, S. Shlosman, Y. Velenik, and V.
Wachtel.